Optimal rates for total variation denoising

2016/03/30 by Hütter, Jan-Christian, Rigollet, Philippe
#62C20 #62G05 #62G08 #62H35 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1603.09388

Abstract

Motivated by its practical success, we show that the two-dimensional total variation denoiser satisfies a sharp oracle inequality that leads to near optimal rates of estimation for a large class of image models such as bi-isotonic, Hölder smooth and cartoons. Our analysis hinges on properties of the unnormalized Laplacian of the two-dimensional grid such as eigenvector delocalization and spectral decay. We also present extensions to more than two dimensions as well as several other graphs.

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